Equating the achievable exponent region to the achievable entropy region by partitioning the source

TL;DR

This paper demonstrates that by partitioning sources, the achievable exponent region can be equated to the entropy region, simplifying analysis in source network problems.

Contribution

It introduces a method to decompose source sets so their image size and entropy characterizations align, enabling broader application of image size techniques.

Findings

Any source set can be partitioned to match entropy characterization.

The number of partitions needed is small, making the equivalence practical.

This approach extends the applicability of image size characterization to complex source networks.

Abstract

In this paper we investigate the image size characterization problem. We show that any arbitrary source set may be decomposed into sets whose image size characterization is the same as its entropy characterization. We also show that the number of these sets required is small enough that one may consider that from a coding perspective the achievable entropy region and achievable exponent region are equal. This has an impact on many source networks and network problems whose solution heretofore could not have the image size characterization applied to them.